Sveinn Björnsson was the only President to die in office. Ásgeir Ásgeirsson was the first President elected by popular vote. Vigdís Finnbogadóttir was the first elected female president in the world. Ólafur Ragnar Grímsson was former populist politician who became president and is the only president to use the authorization to force a national referendum on a law from Althingi the Icelandic parliament.

Sveinn Bjornsson (b. 1881-d. 1952)

Sveinn Björnsson was the first president of Iceland. Born in Copenhagen to Icelandic parents Sveinn became a lawyer and member of Alþingi, the Icelandic parliament, and was known to the Icelandic public as minister.
From 1920 -1941 Sveinn Bjornsson was the Icelandic ambassador in Copenhagen and in fact represented Iceland as a trade-and foreign minister. After Denmark was occupied by Nazi Germany in 1941, Iceland established an office of a „minister to Copenhagen“. The Althing elected Sveinn for the next three years to be the minister.

Just after the birth of the Republic of Iceland in 1944, Sveinn was elected president by the parliament. His first term was only one year as the people of Iceland were to elect their president directly for the first time ever in 1945.

He was, as expected, re-elected in 1945 and again in 1949 without opposition. Sveinn was also co-founder of numerous important businesses and institutions in Iceland, such as Eimskipafélag Íslands The Icelandic Steamship Company, two insurance companies and the Icelandic Red Cross.
Sveinn Bjornsson was married to a Danish woman, Georgia Bjornsson and they had six children. While he was busy fighting for Iceland’s independence, his oldest son, Björn Sv. Björnsson, joined the Nazi’s SS. Sveinn Björnsson died in office in Reykjavík in January 1952.

Asgeir Asgeirsson ( b. 1894 – d. 1972)

Ásgeir Asgeirsson was a theologian and teacher. He married Dóra Þórhallsdóttir in 1917, the daughter of Þórhallur Bjarnarson, fomer bishop of Iceland. Dora´s brother was Tryggvi Þórhallsson, who was Prime Minister of Iceland 1927–1932.

Ásgeir was elected to the Althing in 1923 at the age of 29 and became Minister of Finance in 1931 and Prime Minister in 1932. He remained in the Althing until he was elected president in 1952.
Ásgeir was elected the second President of Iceland in a closely contested election in 1952, which had been called upon early due to the death of Sveinn Björnsson, Iceland's first president. Ásgeir's main opponent, Bjarni Jónsson, minister in the Reykjavík Cathedral, had the endorsement of the governing parties in Iceland, but still Ásgeir managed to prevail.
Ásgeir was re-elected unopposed in 1956, 1960, and 1964. Shortly after his fourth term started, his wife, Dóra, died from leukemia. In 1968 Ásgeir decided not to seek re-election. It was widely expected that his son-in-law, Gunnar Thoroddsen would be elected as his successor, but starting as the frontrunner according to opinion polls, he lost his ground to Kristján Eldjárn.

Kristjan Eldjarn (b.1916 – d. 1982)

Kristjan Eldjarn was the third president of Iceland. Unlike his predecessors, Kristján was not a politician but first and foremost an archaeologist working as teacher and curator of the National Museum. In the late 1960s he was the host of an educational TV series on the then new Icelandic state television (RÚV), in which he showed the audience some museum’s artifacts and explained their historical context. These programs became quite popular and made Kristján a well known and widely respected popular figure.
Starting as the underdog in the 1968 presidential election, running against ambassador Gunnar Thoroddsen who initially had a 70% lead in the opinion polls, Eldjárn won 65.6% of the vote on a 92.2% voter turnout. He was re-elected unopposed in 1972 and 1976. In 1980 he decided not to run for another term, wanting to devote his remaining years entirely to continuing his lifelong academic work.

Vigdis Finnbogadottir (b. 1930 - )

Vigdís Finnbogadóttir is probably the most famous of the Icelandic presidents. One of the reasons for her popularity is that Vigdís (b. 1930) was both Iceland’s and Europe’s first female president reportedly the world’s first democratically elected female head of state.
Having studied French and history of theater she worked as teacher, tour guide and artistic director of the Reykjavík Theater Company for many years. The divorcee later became a working single mother when she adopted a child in 1972.
Vigdís narrowly won the presidential elections in 1980 with 33.6 percent of the national vote, over three male opponents. She was subsequently re-elected three times, unopposed in 1984 and 1992, but with about 95 percent of the votes cast in 1988. During her presidency, Vigdís fought hard for women's rights and thanks to her significant role, gender equality in Iceland is among the highest in the world. She retired in 1996 but remains popular among by the Icelandic people.

Olafur Ragnar Grimsson (b. 1943 -)

Olafur Ragnar Grimsson is the fifth president of Iceland having served since 1996. Ólafur studied economics and political science at the University of Manchester; in 1970 he was the first person from Iceland to earn a PhD in political science. He became a professor of political science at the University of Iceland in 1973.

In 1974 Olafur Ragnar married Gudrun Katrin Thorbergsdottir and a year later she gave birth to twin girls, Gudrun Tinna and Svanhildur Dalla. Gudrun passed away from leukemia in 1998, only two years after Olafur Ragnar was elected president. She was popular among Icelanders and to a large degree credited with his election in 1996. In 2003 Olafur Ragnar married Dorrit Moussaieff, an Israeli-born British jewellry designer, editor and businesswoman. Moussaieff comes from one of the wealthiest families in the UK.
As part of the left-wing People's Alliance, Ólafur was a Member of Althing for Reykjavík from 1978 to 1983. From 1987 - 1995, he was Leader of the People's Alliance; during this time, he served as Minister of Finance from 1988 - 1991 and as a member of Althing from 1991 - 1996. In the 1996 presidential election, he was elected with 41.4% of the votes.
In the 2004 presidential election, Ólafur was re-elected with 67.5% of the votes cast. In the 2008 presidential elections, he was automatically re-elected and sworn in for another term. Ólafur Ragnar announced in March 2012 that he would be seeking a fifth term as the President of Iceland in the 2012 presidential election. Election took place on June 30th and Ólafur received 52.78% of votes cast.